Question

ch 7

Innovation Company is thinking about marketing a new software product. Upfront costs to market and develop the product are $ 4,900,000. The product is expected to generate profits of $ 1,300,000 per year for ten years. The company will have to provide product support expected to cost $ 100,000 per year in perpetuity. Assume all income and expenses occur at the end of each year.

a. What is the NPV of this investment if the cost of capital is 5.77 %​? Should the firm undertake the​ project? Repeat the analysis for discount rates of 1.39 % and 20.33 %​, respectively.

b. How many IRRs does this investment opportunity​ have? ​(Hint​: Consider the two alternative discount rates we used in our analysis in part​ a.)  

c. Can the IRR rule be used to evaluate this​ investment? Explain.

What is the NPV of this investment if the cost of capital is 5.77 %​?

If the cost of capital is 5.77 % the NPV is ​ _________

Answer 1

a. We need to calculate the PV of three different components:

Upfront costs: -$4,900,000

Profits: $1,300,000

Support: $100,000

Present Value (PV) of profits calculated using financial calculator :

Using cost of capital (I/Y) = 5.77%

Number of years (N) = 10years

Future Value (FV) = 0

Annual profits (PMT) = $1,300,000

PV using financial calculator = $9,673,244.866

Present value of support = $100,000 / cost of capital = $100,000 / 5.77% = $1,733,102.25

Net Present Value = Present Value (PV) of profits - Upfront costs - Present value of support

Net Present Value = $9,673,244.86 - $4,900,000 - $1,733,102.25 = $3,040,142.61

Firm should undertake the​ project because of positive NPV of $3,040,142.61.

Present Value (PV) of profits calculated using financial calculator, using discount rate 1.39% :

Using cost of capital (I/Y) = 1.39%

PV using financial calculator = $12,059,005.66

Present value of support = $100,000 / cost of capital = $100,000 / 1.39% = $7,194,244.60

Net Present Value = $12,059,005.66 - $4,900,000 - $7,194,244.60 = -$35,389.4

Firm should not undertake the​ project because of negative NPV of $35,389.4

Present Value (PV) of profits calculated using financial calculator, using discount rate 20.33% :

Using cost of capital (I/Y) = 20.33%

PV using financial calculator = $5,389,720.56

Present value of support = $100,000 / cost of capital = $100,000 / 20.33% = $491,883.91

Net Present Value = $5,389,720.56 - $4,900,000 - $491,883.91 = -$2,1633.50

Firm should not undertake the​ project because of negative NPV of $2,1633.50

b. This has two IRRs which we wouldn’t know unless we had been provided with multiple discount rates in Part (a.). One IRR will be somewhere near 20.33% because at this rate NPV is close to 0 and the other IRR will be near 1.39% because NPV at this rate is -$35,389.40 which is close to 0.

A good rule of thumb though is that If a project has cash outflows during its life or at the end of its life in addition to its initial cash outflow, the project is said to have an unconventional cash flow pattern. Projects with such cash flows may have more than one IRR

c. The IRR rule doesn’t apply when there are multiple IRRs because when there are two or more IRRs, it is not exactly clear which IRR to compare with the hurdle rate because there is a huge difference in two IRRs, one is near 20.33% and other is near 1.39%.

Hurdle rate is the minimum required rate of return which businesses use as a benchmark to decide whether to invest in a project or not.

If the cost of capital is 5.77 % the NPV is $3,040,142.61